Question

Два угла ADC и KDC имеют общую сторону DC.Какую градусную меру может иметь угол ADK,если угол ADC=130 градусов,а угол CDK=30 градусов.

Answer 1

Угол АDK = угол ADC + угол CDK = 130+30=160
Угол АDK = угол ADC - угол CDK = 130-30=100

Answer 2

Problem Analysis

We are given that two angles, ADC and KDC, share a common side DC. We need to determine the measure of angle ADK, given that angle ADC is 130 degrees and angle CDK is 30 degrees.

Solution

To find the measure of angle ADK, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since angles ADC and CDK share the side DC, we can consider triangle ADK.

Let's denote the measure of angle ADK as x. Since the sum of the angles in a triangle is 180 degrees, we can write the equation:

x + 130 + 30 = 180

Simplifying the equation, we have:

x + 160 = 180

Subtracting 160 from both sides, we get:

x = 20

Therefore, the measure of angle ADK is 20 degrees.

Conclusion

The measure of angle ADK, given that angle ADC is 130 degrees and angle CDK is 30 degrees, is 20 degrees.